Finite Group Databasebeta

← #19144419

Subgroups — #19144419

Order 5504.

398 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583526C211yesmaximal, characteristic, complemented
2#14583371C211yesmaximal, characteristic
3#14583202C211yesmaximal, characteristic, complemented
4#14583200C211yesmaximal, characteristic, complemented
5#14583199C211yesmaximal, characteristic, complemented
6#14583197C211yesmaximal, characteristic, complemented
7#14583187C211yesmaximal, characteristic, complemented
8#14583186C211yesmaximal, characteristic, complemented
9#14583178C211yesmaximal, characteristic, complemented
10#14582940C211yesmaximal, characteristic, complemented
11#14582936C211yesmaximal, characteristic, complemented
12#14582924C211yesmaximal, characteristic, complemented
13#14582902C211yesmaximal, characteristic
14#102×D43C211yesmaximal, characteristic
15C43×#474C211yesmaximal, characteristic, complemented
16C2×D4×D43C2211yescharacteristic
17C2×#10621872C2211yescharacteristic
18C2×C8×D43C2211yescharacteristic
19#13063324C2211yescharacteristic, complemented
20#13063323—21no—
21#13063317C2211yescharacteristic, complemented
22#13063316C2211yescharacteristic, complemented
23#13063315—21no—
24#13063303—21no—
25#13063301—21no—
26C4×D172C2211yescharacteristic
27D4×Dic43C2211yescharacteristic
28#13063287C2211yescharacteristic
29C4×C22⋊D43—21no—
30(C22⋊D43)⋊C4—21no—
31#13063283C2211yescharacteristic
32#13063283C2211yescharacteristic
33#13063282C2211yescharacteristic
34C4⋊C4×D43C2211yescharacteristic
35C2×(C2×D43)⋊C4—21no—
36C22⋊C4×D43—21no—
37#13063259C2211yescharacteristic, complemented
38#13063258C2211yescharacteristic, complemented
39#13063257C2211yescharacteristic, complemented
40#13063256C2211yescharacteristic, complemented
41#13063256C2211yescharacteristic, complemented
42#13063256C2211yescharacteristic, complemented
43C4⋊(C43⋊C8)C2211yescharacteristic, complemented
44Dic43⋊C8C2211yescharacteristic, complemented
45Dic43⋊C8C2211yescharacteristic, complemented
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063246C2211yescharacteristic
50#13063245C2211yescharacteristic
51#13063245C2211yescharacteristic
52C4⋊Q8×C43C2211yescharacteristic, complemented
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic, complemented
55#107×C43C2211yescharacteristic, complemented
56C4⋊C8×C43C2211yescharacteristic, complemented
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C23×D43—21no—
60C2×Q8×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C22×Dic43—21no—
65D4×D43—22no—
66D4×D43Q814yescomplemented
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72C2×Dic86—21no—
73C2×C8×C43C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C4⋊C4×C43—21no—
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C22⋊C4×C43—21no—
80C42×C43C2311yescharacteristic
81C22⋊Dic43—21no—
82(C2×D43)⋊C4—21no—
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4D411yescharacteristic
87(C2×D43)⋊C4D411yescharacteristic
88C4⋊Dic43—21no—
89C4⋊Dic43C2311yescharacteristic
90C4⋊Dic43C2311yescharacteristic
91C4⋊Dic43C2311yescharacteristic
92Dic43⋊C4—21no—
93Dic43⋊C4—21no—
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4D411yescharacteristic
98Dic43⋊C4D411yescharacteristic
99C4×Dic43—21no—
100C4×Dic43—21no—
101C4×Dic43C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104#10621872—22no—
105C8×D43—22no—
106C23×C43—21no—
107C22×D43—21no—
108C22×D43—24no—
109C22×D43—81no—
110C22×D43—81no—
111C22×D43C2×D411yescharacteristic
112Q8×C43—81no—
113D4×C43—21no—
114D4×C43C2×Q812yes—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—81no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—24no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—21no—
126C2×Dic43—81no—
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130D172—21no—
131D172C2×Q812yes—
132C4×D43—81no—
133C4×D43—81no—
134C4×D43—81no—
135C4×D43C2×Q812yes—
136C4×D43#4112yes—
137Dic86—81no—
138C8×C43—21no—
139C8×C43—21no—
140C43⋊C8—21no—
141C43⋊C8—21no—
142C22×C43—22no—
143C22×C43—41no—
144C22×C43—41no—
145C22×C43C22×D411yescharacteristic
146C2×D43—21no—
147C2×D43—21no—
148C2×D43—22no—
149C2×D43—41no—
150C2×D43—41no—
151C2×D43—84no—
152C2×D43C22⋊Q812yes—
153C4×C43—21no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C22×Q811yescharacteristic
159C4×C43C2×#4111yescharacteristic
160Dic43—21no—
161Dic43—21no—
162Dic43—41no—
163Dic43—41no—
164Dic43—41no—
165Dic43C22⋊Q812yes—
166#3081—431nomaximal, Sylow
167C2×C43—42no—
168C2×C43C2×C22⋊Q811yescharacteristic
169C2×C43#57611yescharacteristic
170C2×C43#57711yescharacteristic
171D43—22no—
172D43—42no—
173#544—431no—
174#518—431no—
175#478—431no—
176#478—431no—
177#478—431no—
178#478—431no—
179#476—431no—
180#476—431no—
181#474—431no—
182#474D4311yescharacteristic, complemented
183#428—431no—
184#427—431no—
185#424—431no—
186#418—431no—
187C2×#102—431no—
188C43#308111yescharacteristic, complemented, Sylow
189C22×D4—431no—
190C2×M16—431no—
191C22×C8—431no—
192C4⋊Q8—431no—
193C4⋊Q8—861no—
194C4⋊Q8C2×D4311yescharacteristic, complemented
195#125—431no—
196#125—431no—
197#125—861no—
198C22⋊Q8—861no—
199C22⋊Q8—861no—
200C4×D4—431no—
201C4×D4—431no—
202C4×D4—431no—
203C4×D4—861no—
204C4×D4—861no—
205C4×D4C2×D4311yescharacteristic
206#117—431no—
207#117—431no—
208#117—431no—
209C2×C4⋊C4—431no—
210C2×C22⋊C4—861no—
211C2×C22⋊C4—861no—
212#107—431no—
213#107—431no—
214#107C2×D4311yescharacteristic, complemented
215#107C2×D4311yescharacteristic, complemented
216#106—431no—
217#106—431no—
218#106—431no—
219#106—431no—
220C4⋊C8—431no—
221C4⋊C8—431no—
222C4⋊C8—431no—
223C4⋊C8C2×D4311yescharacteristic, complemented
224#102—431no—
225#102—431no—
226#102—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230#102C2×D4311yescharacteristic
231#102C2×D4311yescharacteristic
232C24—861no—
233C2×Q8—21no—
234C2×Q8—861no—
235C2×D4—434no—
236C2×D4—431no—
237C2×D4—862no—
238C2×D4—861no—
239C2×D4C22×D4311yescharacteristic
240C22×C4—21no—
241C22×C4—431no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4—861no—
246M16—862no—
247C2×C8—431no—
248C2×C8—431no—
249C2×C8—862no—
250C2×C8C22×D4311yescharacteristic
251C2×C8C22×D4311yescharacteristic
252C4⋊C4—21no—
253C4⋊C4—431no—
254C4⋊C4—431no—
255C4⋊C4—431no—
256C4⋊C4—431no—
257C4⋊C4—431no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4—861no—
264C4⋊C4C22×D4311yescharacteristic
265C4⋊C4C22×D4311yescharacteristic
266C4⋊C4C22×D4311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—431no—
269C22⋊C4—431no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C42—431no—
276C42—861no—
277C42—861no—
278C42C22×D4311yescharacteristic
279C23—21no—
280C23—431no—
281C23—864no—
282C23—861no—
283C23—3441no—
284C23—3441no—
285Q8—81no—
286Q8—3441no—
287D4—21no—
288D4—432no—
289D4—864no—
290D4—861no—
291D4Q8×D4312yes—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—81no—
296C2×C4—431no—
297C2×C4—432no—
298C2×C4—432no—
299C2×C4—431no—
300C2×C4—431no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—3441no—
305C2×C4—3441no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4D4×D4311yescharacteristic
309C2×C4D4×D4311yescharacteristic
310C2×C4C23×D4311yescharacteristic
311C8—21no—
312C8—21no—
313C8—861no—
314C8—861no—
315C22—22no—
316C22—41no—
317C22—41no—
318C22—432no—
319C22—861no—
320C22—861no—
321C22—862no—
322C22—3444no—
323C22—1721no—
324C22—1721no—
325C22C2×D4×D4311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—432no—
332C4—861no—
333C4—861no—
334C4—1721no—
335C4—1721no—
336C4—1721no—
337C4C2×Q8×D4311yescharacteristic
338C4#41×D4311yescharacteristic
339C2—42no—
340C2—862no—
341C2—1722no—
342C2C22⋊Q8×D4311yescharacteristic
343C2#1458370011yescharacteristic
344C2#1458370811yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#474C2
socleC22×C43C22×D4
hypercenter#474D43
hypocenterC43#3081
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #14583526C2semidirect
3. #14583202C2semidirect
4. #14583200C2semidirect
5. #14583199C2semidirect
6. #14583197C2semidirect
7. #14583187C2semidirect
8. #14583186C2semidirect
9. #14583178C2semidirect
10. #14582940C2semidirect
11. #14582936C2semidirect
12. #14582924C2semidirect
15. C43×#474C2semidirect
19. #13063324C22semidirect
21. #13063317C22semidirect
22. #13063316C22semidirect
37. #13063259C22semidirect
38. #13063258C22semidirect
39. #13063257C22semidirect
40. #13063256C22semidirect
41. #13063256C22semidirect
42. #13063256C22semidirect
43. C4⋊(C43⋊C8)C22semidirect
44. Dic43⋊C8C22semidirect
45. Dic43⋊C8C22semidirect
52. C4⋊Q8×C43C22semidirect
54. #107×C43C22semidirect
55. #107×C43C22semidirect
56. C4⋊C8×C43C22semidirect
66. D4×D43Q8semidirect
182. #474D43semidirect
188. C43#3081semidirect
194. C4⋊Q8C2×D43semidirect
214. #107C2×D43semidirect
215. #107C2×D43semidirect
223. C4⋊C8C2×D43semidirect